What is the length of BC, rounded to the nearest tenth?

13.0 units, 28.8 units, 31.2 units, 33.8 units

Solution:

In a right triangle ADB

AB² = AD² + BD²

AD = 5 units and BD = 12 units

AB² = 5² + 12²

AB² = 169

AB = 13 units

In a right triangle ADB

cos BAD = adjacent side/ hypotenuse

Substituting the values

cos BAD = AD/AB = 5/13

In a right triangle ABC

cos BAD = cos BAC = 5/13

cos BAC = adjacent side/hypotenuse

cos BAC = AB/AC

5/13 = AB/AC

5/13 = 13/AC

AC = (13 × 13)/5

AC = 33.8 units

We know that

DC = AC - AD

Substituting the values

DC = 33.8 - 5

DC = 28.8 units

Here

BC² = BD² + DC²

Substituting the values

BC² = 12² + 28.8²

BC² = 973.44

BC = 31.2 units

Therefore, the length of BC is 31.2 units.

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What is the length of BC, rounded to the nearest tenth?
13.0 units, 28.8 units, 31.2 units, 33.8 units

Summary:

The length of BC is 31.2 units, rounded to the nearest tenth.